If we label the generations of cells turned ON by consecutive numbers we get the cell pattern shown below:

9...9...9...9...9

.888.888.888.888.

.878.878.878.878.

.886668666866688.

9..656.656.656..9

.886644464446688.

.878.434.434.878.

.886644222446688.

9..656.212.656..9

.886644222446688.

.878.434.434.878.

.886644464446688.

9..656.656.656..9

.886668666866688.

.878.878.878.878.

.888.888.888.888.

9...9...9...9...9

At the first generation, only the central "1" is ON, so a(1) = 1. At the second generation, we turn ON eight cells around the central cell, leading to a(2) = a(1)+8 = 9. At the third generation, we turn ON four peninsula cells, so a(3) = a(2)+4 = 13. At the fourth generation, we turn ON the cells around the cells turned ON at the third generation, so a(4) = a(3)+28 = 41. At the 5th generation, we turn ON four peninsula cells and four bridge cells, so a(5) = a(4)+8 = 49.